Particle Accelerator Physics

✍ Scribed by Helmut Wiedemann

• Publisher: Springer
• Year: 2024
• Tongue: English
• Leaves: 1029
• Category: Library

✦ Synopsis

This book by Helmut Wiedemann is a well-established, classic text, providing an in-depth and comprehensive introduction to the field of high-energy particle acceleration and beam dynamics. The present 4th edition has been significantly revised, updated and expanded. The newly conceived Part I is an elementary introduction to the subject matter for undergraduate students. Part II gathers the basic tools in preparation of a more advanced treatment, summarizing the essentials of electrostatics and electrodynamics as well as of particle dynamics in electromagnetic fields. Part III is an extensive primer in beam dynamics, followed, in Part IV, by an introduction and description of the main beam parameters and including a new chapter on beam emittance and lattice design. Part V is devoted to the treatment of perturbations in beam dynamics. Part VI then discusses the details of charged particle acceleration. Parts VII and VIII introduce the more advanced topics of coupled beam dynamics and describe very intense beams – a number of additional beam instabilities are introduced and reviewed in this new edition. Part IX is an exhaustive treatment of radiation from accelerated charges and introduces important sources of coherent radiation such as synchrotrons and free-electron lasers. The appendices at the end of the book gather useful mathematical and physical formulae, parameters and units. Solutions to many end-of-chapter problems are given. This textbook is suitable for an intensive two-semester course starting at the senior undergraduate level.

✦ Table of Contents

Preface to Fourth Edition
Preface to Third Edition
Preface to First Edition, Volume I
Preface to First Edition, Volume II
Contents
Part I Introduction
1 Introduction to Accelerator Physics
1.1 Short Historical Overview
1.2 Particle Accelerator Systems
1.2.1 Main Components of Accelerator Facilities
1.2.2 Applications of Particle Accelerators
1.3 Definitions and Formulas
1.3.1 Units and Dimensions
1.3.2 Maxwell's Equations
1.4 Primer in Special Relativity
1.4.1 Lorentz Transformation
Lorentz Transformation of Fields
Lorentz Contraction
Time Dilatation
1.4.2 Lorentz Invariance
Invariance to Lorentz Transformations
Space-Time
Four-Velocity
Four-Acceleration
Momentum-Energy 4-Vector
Photon 4-Vector
Force 4-Vector
Electro-magnetic 4-Vector
1.4.3 Spatial and Spectral Distribution of Radiation
Spectral Distribution
Spatial Distribution
1.4.4 Particle Collisions at High Energies
1.5 Principles of Particle-Beam Dynamics
1.5.1 Electromagnetic Fields of Charged Particles
Electric Field of a Point Charge
Fields of a Charged Particle Beam
1.5.2 Vector and Scalar Potential
1.5.3 Wave Equation
Lienard-Wiechert Potentials
1.5.4 Induction
1.5.5 Lorentz Force
1.5.6 Equation of Motion
1.5.7 Charged Particles in an Electromagnetic Field
1.5.8 Linear Equation of Motion
1.5.9 Energy Conservation
Poynting Vector
1.5.10 Stability of a Charged-Particle Beam
Problems
References
2 Linear Accelerators
2.1 Principles of Linear Accelerators
2.1.1 Charged Particles in Electric Fields
2.1.2 Electrostatic Accelerators
Cascade Generators
Van de Graaff Accelerator
2.2 Electric Field Components
2.2.1 Electrostatic Deflectors
2.2.2 Electrostatic Focusing Devices
2.2.3 Iris Doublet
2.2.4 Einzellens
2.3 Acceleration by rf Fields
2.3.1 Basic Principle of Microwave Linear Accelerators
Synchronicity Condition
Problems
References
3 Circular Accelerators
3.1 Betatron
3.2 Weak Focusing
3.3 Adiabatic Damping
3.4 Acceleration by rf Fields
3.4.1 Microtron
3.4.2 Cyclotron
3.4.3 Synchro-Cyclotron
3.4.4 Isochron Cyclotron
3.4.5 Synchrotron
3.4.6 Storage Ring
3.4.7 Summary of Characteristic Parameters
Problems
References
Part II Tools We Need
4 Elements of Classical Mechanics
4.1 How to Formulate a Lagrangian?
4.1.1 The Lagrangian for a Charged Particlein an EM-Field
4.2 Lorentz Force
4.3 Frenet-Serret Coordinates
4.4 Hamiltonian Formulation
4.4.1 Cyclic Variables
4.4.2 Canonical Transformations
4.4.3 Curvilinear Coordinates
4.4.4 Extended Hamiltonian
4.4.5 Change of Independent Variable
Problems
References
5 Particle Dynamics in Electro-Magnetic Fields
5.1 The Lorentz Force
5.2 Fundamentals of Charged Particle Beam Optics
5.2.1 Particle Beam Guidance
5.2.2 Particle Beam Focusing
5.3 Equation of Motion
5.4 Equations of Motion from the Lagrangian and Hamiltonian
5.4.1 Equations of Motion from Lagrangian
5.4.2 Canonical Momenta
5.4.3 Equation of Motion from Hamiltonian
5.4.4 Harmonic Oscillator
5.4.5 Action-Angle Variables
5.5 Solutions of the Linear Equations of Motion
5.5.1 Linear Unperturbed Equation of Motion
5.5.2 Matrix Formulation
5.5.3 Wronskian
5.5.4 Perturbation Terms
Dispersion Function
Problems
References
6 Electromagnetic Fields
6.1 Pure Multipole Field Expansion
6.1.1 Electromagnetic Potentials and Fields for Beam Dynamics
6.1.2 Fields, Gradients and Multipole Strength Parameter
6.1.3 Main Magnets for Beam Dynamics
Deflecting Magnets
Focusing Device
Synchrotron Magnet
Higher Order Multipole Magnets
Vacuum Chamber Material
6.1.4 Multipole Misalignment and ``Spill-down''
6.2 Main Magnet Design Criteria
6.2.1 Design Characteristics of Dipole Magnets
Excitation Current and Saturation in a Bending Magnet
6.2.2 Quadrupole Design Concepts
Pole Profile Shimming
Excitation Current and Saturation
6.3 Magnetic Field Measurement
6.3.1 Hall Probe
6.3.2 Rotating Coil
Practical Considerations
6.4 General Transverse Magnetic-Field Expansion
6.4.1 Pure Multipole Magnets
6.4.2 Kinematic Terms
6.5 Third-Order Differential Equation of Motion
6.6 Longitudinal Field Devices
6.7 Periodic Wiggler Magnets
6.7.1 Wiggler Field Configuration
6.8 Electrostatic Quadrupole
Problems
References
Part III Beam Dynamics
7 Single Particle Dynamics
7.1 Linear Beam Transport Systems
7.1.1 Nomenclature
7.2 Matrix Formalism in Linear Beam Dynamics
7.2.1 Driftspace
7.2.2 Quadrupole Magnet
7.2.3 Thin Lens Approximation
7.2.4 Quadrupole End Field Effects
7.3 Focusing in Bending Magnets
7.3.1 Sector Magnets
7.3.2 Fringe Field Effects
7.3.3 Finite Pole Gap
7.3.4 Wedge Magnets
7.3.5 Rectangular Magnet
7.3.6 Focusing in a Wiggler Magnet
7.3.7 Hard-Edge Model of Wiggler Magnets
7.4 Elements of Beam Dynamics
7.4.1 Building Blocks for Beam Transport Lines
General Focusing Properties
Chromatic Properties
Achromatic Lattices
7.4.2 Isochronous Systems
Problems
References
8 Particle Beams and Phase Space
8.1 Beam Emittance
8.1.1 Liouville's Theorem
8.1.2 Transformation in Phase Space
8.1.3 Beam Matrix
Measurement of the Beam Emittance
8.2 Betatron Functions
8.2.1 Beam Envelope
8.3 Beam Dynamics in Terms of Betatron Functions
8.3.1 Beam Dynamics in Normalized Coordinates
8.4 Dispersive Systems
8.4.1 Analytical Solution
8.4.2 33-Transformation Matrices
8.4.3 Linear Achromat
8.4.4 Spectrometer
8.4.5 Measurement of Beam Energy Spectrum
8.4.6 Path Length and Momentum Compaction
Problems
References
9 Longitudinal Beam Dynamics
9.1 Longitudinal Particle Motion
9.1.1 Longitudinal Phase Space Dynamics
9.2 Equation of Motion in Phase Space
9.2.1 Small Oscillation Amplitudes
9.2.2 Phase Stability
Large Oscillation Amplitudes
9.2.3 Acceleration of Charged Particles
9.3 Longitudinal Phase Space Parameters
9.3.1 Separatrix Parameters
9.3.2 Momentum Acceptance
9.3.3 Bunch Length
9.3.4 Longitudinal Beam Emittance
9.3.5 Phase Space Matching
9.4 Higher-Order Phase Focusing
9.4.1 Dispersion Function in Higher Order
9.4.2 Path Length in Higher Order
9.4.3 Higher Order Momentum Compaction Factor
9.4.4 Higher-Order Phase Space Motion
9.4.5 Stability Criteria
Problems
References
10 Periodic Focusing Systems
10.1 FODO Lattice
10.1.1 Scaling of FODO Parameters
10.1.2 Betatron Motion in Periodic Structures
Stability Criterion
10.1.3 General FODO Lattice
10.2 Beam Dynamics in Periodic Closed Lattices
10.2.1 Hill's Equation
10.2.2 Periodic Betatron Functions
10.2.3 Periodic Dispersion Function
Scaling of the Dispersion in a FODO Lattice
General Solution for the Periodic Dispersion
10.2.4 Periodic Lattices in Circular Accelerators
Synchrotron Lattice
Phase Space Matching
Dispersion Matching
Magnet Free Insertions
Low Beta Insertions
10.3 FODO Lattice and Acceleration
10.3.1 Lattice Structure
10.3.2 Transverse Beam Dynamics and Acceleration
Analytical Solutions
Transformation Matrices
Adiabatic Damping
Problems
References
Part IV Beam Parameters
11 Particle Beam Parameters
11.1 Definition of Beam Parameters
11.1.1 Beam Energy
11.1.2 Time Structure
11.1.3 Beam Current
11.1.4 Beam Dimensions
11.2 Damping
11.2.1 Robinson Criterion
11.3 Particle Distribution in Longitudinal Phase Space
11.3.1 Energy Spread
11.3.2 Bunch Length
11.4 Transverse Beam Emittance
11.4.1 Equilibrium Beam Emittance
11.4.2 Emittance Increase in a Beam Transport Line
11.4.3 Vertical Beam Emittance
11.4.4 Beam Sizes
11.4.5 Beam Divergence
11.5 Variation of the Damping Distribution
11.5.1 Damping Partition and Rf-Frequency
11.6 Variation of the Equilibrium Beam Emittance
11.6.1 Beam Emittance and Wiggler Magnets
11.6.2 Damping Wigglers
11.7 Robinson Wiggler
11.7.1 Damping Partition and Synchrotron Oscillation
11.7.2 Can We Eliminate the Beam Energy Spread?
11.8 Beam Life Time
11.8.1 Beam Lifetime and Vacuum
Elastic Scattering
Inelastic Scattering
11.8.2 Ultra High Vacuum System
Thermal Gas Desorption
Synchrotron Radiation Induced Desorption
Problems
References
12 Vlasov and Fokker–Planck Equations
12.1 The Vlasov Equation
12.1.1 Betatron Oscillations and Perturbations
12.1.2 Damping
12.2 Damping of Oscillations in Electron Accelerators
12.2.1 Damping of Synchrotron Oscillations
12.2.2 Damping of Vertical Betatron Oscillations
12.2.3 Robinson's Damping Criterion
12.2.4 Damping of Horizontal Betatron Oscillations
12.3 The Fokker–Planck Equation
12.3.1 Stationary Solution of the Fokker–Planck Equation
12.3.2 Particle Distribution within a Finite Aperture
12.3.3 Particle Distribution in the Absence of Damping
Problems
References
13 Equilibrium Particle Distribution
13.1 Particle Distribution in Phase Space
13.1.1 Diffusion Coefficient and Synchrotron Radiation
13.1.2 Quantum Excitation of Beam Emittance
13.2 Equilibrium Beam Emittance
13.2.1 Horizontal Equilibrium Beam Emittance
13.2.2 Vertical Equilibrium Beam Emittance
13.3 Equilibrium Energy Spread and Bunch Length
13.3.1 Equilibrium Beam Energy Spread
13.3.2 Equilibrium Bunch Length
13.4 Phase-Space Manipulation
13.4.1 Exchange of Transverse Phase-Space Parameters
13.4.2 Bunch Compression
13.4.3 Alpha Magnet
13.5 Polarization of a Particle Beam
Problems
References
14 Beam Emittance and Lattice Design
14.1 Equilibrium Beam Emittance in Storage Rings
14.1.1 FODO Lattice
14.1.2 Minimum Beam Emittance
14.2 Absolute Minimum Emittance
14.3 Beam Emittance in Periodic Lattices
14.3.1 The Double Bend Achromat Lattice (DBA)
14.3.2 The FODO Lattice
14.3.3 Optimum Emittance for Colliding Beam Storage Rings
Problems
References
Part V Perturbations
15 Perturbations in Beam Dynamics
15.1 Magnet Field and Alignment Errors
15.1.1 Self Compensation of Perturbations
15.2 Dipole Field Perturbations
15.2.1 Dipole Field Errors and Dispersion Function
15.2.2 Perturbations in Open Transport Lines
15.2.3 Existence of Equilibrium Orbits
15.2.4 Closed Orbit Distortion
15.2.5 Statistical Distribution of Dipole Field and Alignment Errors
15.2.6 Dipole Field Errors in Insertion Devices
15.2.7 Closed Orbit Correction
15.2.8 Response Matrix
15.2.9 Orbit Correction with Single Value Decomposition ( SVD)
Single Value Decomposition (SVD)
15.3 Quadrupole Field Perturbations
15.3.1 Betatron Tune Shift
15.3.2 Optics Perturbation Due to Insertion Devices
15.3.3 Resonances and Stop Band Width
15.3.4 Perturbation of Betatron Function
15.4 Chromatic Effects in a Circular Accelerator
15.4.1 Chromaticity
15.4.2 Chromaticity Correction
15.4.3 Chromaticity in Higher Approximation
15.4.4 Non-linear Chromaticity
15.5 Kinematic Perturbation Terms
15.6 Perturbation Methods in Beam Dynamics
15.6.1 Periodic Distribution of Statistical Perturbations
15.6.2 Periodic Perturbations in Circular Accelerators
15.6.3 Statistical Methods to Evaluate Perturbations
15.7 Control of Beam Size in Transport Lines
Problems
References
16 Resonances
16.1 Lattice Resonances
16.1.1 Resonance Conditions
16.1.2 Coupling Resonances
16.1.3 Resonance Diagram
16.2 Hamiltonian Resonance Theory
16.2.1 Non-linear Hamiltonian
16.2.2 Resonant Terms
16.2.3 Resonance Patterns and Stop-Band Width
16.2.4 Half-Integer Stop-Band
16.2.5 Separatrices
16.2.6 General Stop-Band Width
16.3 Third-Order Resonance
16.3.1 Particle Motion in Phase Space
Problems
References
17 Hamiltonian Nonlinear Beam Dynamics
17.1 Higher-Order Beam Dynamics
17.1.1 Multipole Errors
17.1.2 Non-linear Matrix Formalism
17.2 Aberrations
17.2.1 Geometric Aberrations
Compensation of Nonlinear Perturbations
Sextupoles Separated by a -I-Transformation
17.2.2 Filamentation of Phase Space
17.2.3 Chromatic Aberrations
17.2.4 Particle Tracking
17.3 Hamiltonian Perturbation Theory
17.3.1 Tune Shift in Higher Order
Problems
References
Part VI Acceleration
18 Charged Particle Acceleration
18.1 Rf-Waveguides and Cavities
18.1.1 Wave Equation
18.1.2 Rectangular Waveguide Modes
18.1.3 Cylindrical Waveguide Modes
TM-Mode Field Components in Cylindrical Waveguides
18.2 Rf-Cavities
18.2.1 Square Cavities
18.2.2 Cylindrical Cavity
18.2.3 Energy Gain
18.2.4 Rf-Cavity as an Oscillator
18.2.5 Cavity Losses and Shunt Impedance
18.3 Rf-Parameters
18.3.1 Synchronous Phase and Rf-voltage
18.4 Linear Accelerator
18.4.1 Basic Waveguide Parameters
18.4.2 Particle Capture in a Linear Accelerator Field
18.5 Preinjector and Beam Preparation
18.5.1 Prebuncher
18.5.2 Beam Chopper
18.5.3 Buncher Section
Problems
References
19 Beam-Cavity Interaction
19.1 Coupling Between rf-Field and Particles
19.1.1 Network Modelling of an Accelerating Cavity
19.2 Beam Loading and Rf-System
19.3 Higher-Order Mode Losses in an Rf-Cavity
19.3.1 Efficiency of Energy Transfer from Cavity to Beam
19.4 Beam Loading
19.5 Phase Oscillation and Stability
19.5.1 Robinson Damping
19.5.2 Potential Well Distortion
Problems
References
Part VII Coupled Motion
20 Dynamics of Coupled Motion
20.1 Equations of Motion in Coupled Systems
20.1.1 Coupled Beam Dynamics in Skew Quadrupoles
20.1.2 Particle Motion in a Solenoidal Field
20.1.3 Transformation Matrix for a Solenoid Magnet
20.2 Betatron Functions for Coupled Motion
20.3 Conjugate Trajectories
20.4 Hamiltonian and Coupling
20.4.1 Linearly Coupled Motion
Linear Difference Resonance
Linear Sum Resonance
20.4.2 Higher-Order Coupling Resonances
20.4.3 Multiple Resonances
Problems
References
Part VIII Intense Beams
21 Statistical and Collective Effects
21.1 Statistical Effects
21.1.1 Schottky Noise
21.1.2 Stochastic Cooling
21.1.3 Touschek Effect
21.1.4 Intra-Beam Scattering
21.2 Collective Self Fields
21.2.1 Self Field for Elliptical Particle Beams
Forces from Space-Charge Fields
21.2.2 Beam–Beam Effect
21.2.3 Transverse Self Fields
21.2.4 Fields from Image Charges
21.2.5 Space-Charge Effects
Space Charge Dominated Beams
Space-Charge Tune Shift
21.2.6 Longitudinal Space-Charge Field
21.3 Beam-Current Spectrum
21.3.1 Longitudinal Beam Spectrum
21.3.2 Transverse Beam Spectrum
Problems
References
22 Wake Fields and Instabilities
22.1 Definitions of Wake Field and Impedance
22.1.1 Parasitic Mode Losses and Impedances
22.1.2 Longitudinal Wake Fields
Loss Parameter
22.1.3 Transverse Wake Fields
22.1.4 Panofsky-Wenzel Theorem
22.2 Impedances in an Accelerator Environment
22.2.1 Space-Charge Impedance
22.2.2 Resistive-Wall Impedance
22.2.3 Cavity-Like Structure Impedance
22.2.4 Overall Accelerator Impedance
22.2.5 Broad-Band Wake Fields in a Linear Accelerator
22.3 Coasting-Beam Instabilities
22.3.1 Negative-Mass Instability
22.3.2 Dispersion Relation
22.3.3 Landau Damping
22.3.4 Transverse Coasting-Beam Instability
22.4 Longitudinal Single-Bunch Effects
22.4.1 Potential-Well Distortion
Synchrotron Oscillation Tune Shift
Bunch Lengthening
22.5 Transverse Single-Bunch Instabilities
22.5.1 Beam Break-Up in Linear Accelerators
22.5.2 Fast Head-Tail Effect
Measurement of the Broad-Band Impedance
22.5.3 Head-Tail Instability
22.6 Multi-Bunch Instabilities
Problems
References
Part IX Synchrotron Radiation
23 Fundamental Processes
23.1 Radiation from Moving Charges
23.1.1 Why Do Charged Particles Radiate?
23.1.2 Spontaneous Synchrotron Radiation
23.1.3 Stimulated Radiation
23.1.4 Electron Beam
23.2 Conservation Laws and Radiation
23.2.1 Cherenkov Radiation
23.2.2 Compton Radiation
23.3 Electromagnetic Radiation
23.3.1 Coulomb Regime
23.3.2 Radiation Regime
Problems
References
24 Overview of Synchrotron Radiation
24.1 Radiation Sources
24.1.1 Bending Magnet Radiation
24.1.2 Superbends
24.1.3 Wavelength Shifter
24.1.4 Wiggler Magnet Radiation
24.1.5 Undulator Radiation
Back Scattered Photons
Photon Flux
24.2 Radiation Power
24.3 Spectrum
24.4 Spatial Photon Distribution
24.5 Fraunhofer Diffraction
24.6 Spatial Coherence
24.7 Temporal Coherence
24.8 Spectral Brightness
24.8.1 Matching
24.9 Photon Source Parameters
Problems
References
25 Theory of Synchrotron Radiation
25.1 Radiation Field
25.2 Total Radiation Power and Energy Loss
25.2.1 Transition Radiation
25.3 Spatial Radiation Distribution
25.3.1 Radiation Lobes
25.4 Radiation Field in the Frequency Domain
25.4.1 Spectral Distribution in Space and Polarization
25.4.2 Spectral and Spatial Photon Flux
25.4.3 Harmonic Representation
25.4.4 Spatial Radiation Power Distribution
25.5 Asymptotic Solutions
25.5.1 Low Frequencies and Small Observation Angles
25.5.2 High Frequencies or Large Observation Angles
25.6 Angle-Integrated Spectrum
25.7 Statistical Radiation Parameters
Problems
References
26 Insertion Device Radiation
26.1 Particle Dynamics in a Periodic Field Magnet
26.2 Undulator Radiation
26.2.1 Fundamental Wavelength
26.2.2 Radiation Power
26.2.3 Spatial and Spectral Distribution
26.2.4 Line Spectrum
26.2.5 Spectral Undulator Brightness
26.3 Elliptical Polarization
26.3.1 Elliptical Polarization from Bending MagnetRadiation
26.3.2 Elliptical Polarization from Periodic InsertionDevices
Asymmetric Wiggler Magnet
Elliptically Polarizing Undulator
Problems
References
27 Free Electron Lasers
27.1 Small Gain Regime
27.1.1 Energy Transfer
27.1.2 Equation of Motion
27.1.3 FEL-Gain
27.2 High Gain Free Electron Laser
27.2.1 Electron Dynamics in a SASE FEL
27.2.2 Electron Source
27.2.3 Beam Dynamics
27.2.4 Undulator
Problems
References
Correction to: Particle Accelerator Physics
Solutions
Solutions for Chap. 1
Solutions for Chap. 2
Solutions for Chap. 3
Solutions for Chap. 4
Solutions for Chap. 5
Solutions for Chap. 6
Solutions for Chap. 7
Solutions for Chap. 8
Solutions for Chap. 9
Solutions for Chap. 10
Solutions for Chap. 11
Solutions for Chap. 12
Solutions for Chap. 13
Solutions for Chap. 14
Solutions for Chap. 15
Solutions for Chap. 16
Solutions for Chap. 17
Solutions for Chap. 18
Solutions for Chap. 19
Solutions for Chap. 20
Solutions for Chap. 21
Solutions for Chap. 22
Solutions for Chap. 23
Solutions for Chap. 24
Solutions for Chap. 25
Solutions for Chap. 26
Solutions for Chap. 27
A Useful Mathematical Formulae
A.1 Vector Algebra
A.1.1 Differential Vector Expressions
A.1.2 Algebraic Relations
A.1.3 Differential Relations
A.1.4 Partial Integration
A.1.5 Trigonometric and Exponential Functions
A.1.6 Integral Relations
A.1.7 Dirac's Delta Function
A.1.8 Bessel's Functions
A.1.9 Series Expansions
A.1.10 Fourier Series
Parseval's Theorem
Fourier Transform
A.1.11 Coordinate Transformations
Cartesian coordinates
General Coordinate Transformation
Cylindrical Coordinates
Polar Coordinates
Curvilinear Coordinates
B Physical Formulae and Parameters
B.1 Physical Constants
B.2 Relations of Fundamental Parameters
B.3 Unit Conversions
B.4 Maxwell's Equations
B.5 Wave and Field Equations
B.6 Relativistic Relations
B.6.1 Lorentz Transformation
B.6.2 Four-Vectors
B.6.3 Square of the 4-Acceleration
B.6.4 Miscellaneous 4-Vectors and Lorentz Invariant Properties
B.7 Transformation Matrices in Beam Dynamics
B.8 General Transformation Matrix
B.8.1 Symmetric Magnet Arrangement
B.8.2 Inverse Transformation Matrix
B.9 Specific Transformation Matrices
B.9.1 Drift Space
B.9.2 Bending Magnets
Sector Magnet
Wedge Magnet
Rectangular Magnet
Synchrotron Magnet (Sector Type)
Synchrotron Magnet (Rectangular Type)
B.9.3 Quadrupole
Focusing Quadrupole ( k0>0,φ=k l )
Defocusing Quadrupole (k<0,φ="026A30C k"026A30C )
Quadrupole Doublet
Quadrupole Triplet
Index